When a public highway, street, or road extends into or through a public trail, trail area, greenway, or park area of a district, or when a public highway, street, or road forms all or part of a suitable connection between two or more public trails, trail areas, or park areas within a district, and it is advisable by the board to make alterations in the route or width of the highway or to grade, drain, pave, or otherwise improve the highway, the board may enter into agreements, consistent with the purposes of that district, with the public authorities in control of the portion of the highway, street, or road that lies within any, or forms any part of, a connecting link to and between any, public trail, trail area, or park area of a district. Any agreement with any such public authority shall follow the procedure authorized by law for dealing with that authority, and any agreement shall provide for the payment by the board of an agreed-upon portion of the costs of that agreement. This section shall not alter the legal status of that highway, street, or road in any way.